Theorem bj-ssbbii 33160

Description: Biconditional property for substitution. Uses only ax-1--5. (Contributed by BJ, 22-Dec-2020.)

Hypothesis

Ref	Expression
bj-ssbbii.1	⊢ (𝜑 ↔ 𝜓)

Assertion

Ref	Expression
bj-ssbbii	⊢ ([𝑡/𝑥]b𝜑 ↔ [𝑡/𝑥]b𝜓)

Proof of Theorem bj-ssbbii

Step	Hyp	Ref	Expression
1		bj-ssbbi 33158	. 2 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → ([𝑡/𝑥]b𝜑 ↔ [𝑡/𝑥]b𝜓))
2		bj-ssbbii.1	. 2 ⊢ (𝜑 ↔ 𝜓)
3	1, 2	mpg 1896	1 ⊢ ([𝑡/𝑥]b𝜑 ↔ [𝑡/𝑥]b𝜓)

Syntax hints:   ↔ wb 198  [wssb 33155

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1894  ax-4 1908  ax-5 2009

This theorem depends on definitions:  df-bi 199  df-ssb 33156

This theorem is referenced by:  bj-ssbssblem  33184  bj-ssbcom3lem  33185